Teague, the 31st overall pick of the 2012 NBA Draft, has not established himself with the Bulls. He appeared in 19 games with them, but has also spent time with their affiliate in the NBA Development League.

Shengelia, a second-round pick in 2012, saw limited minutes in 17 games this season and was expected to be the odd man out as Paul Pierce and other Nets returned from injuries. Like Teague, he has spent time in the D-League.

Teague is expected to provide depth for the Nets as they await Deron Williams' return from ankle surgery.

Most reports say the Bulls will benefit most from removing Teague's salary, which will allow them to stay under the NBA's luxury-tax ceiling.

Taylor, also a 2012 second-rounder, will add to New Orleans' backcourt depth while Jrue Holiday recovers from a broken leg. Taylor averaged 11.7 minutes in 23 games this season for Brooklyn.